A015334 Gaussian binomial coefficient [ n,6 ] for q = -11.

1, 1623931, 2900866919644, 5135204548028317764, 9097949506151746630368210, 16117472448301015835209097979510, 28553101725457044215054700034776694620

Offset: 6

Author

Olivier Gérard, Dec 11 1999

Keywords

• nonn
• easy

References

• J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
• I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
• M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 6..100

Programs

Magma

/* By definition: */ r:=6; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..12]]; // Bruno Berselli, Oct 30 2012

Mathematica

Table[QBinomial[n, 6, -11], {n, 6, 10}] (* Vincenzo Librandi, Oct 29 2012 *)

Sage

[gaussian_binomial(n,6,-11) for n in range(6,13)] # Zerinvary Lajos, May 27 2009

Formula

G.f.: x^6/((1-x)*(1+11*x)*(1-121*x)*(1+1331*x)*(1-14641*x)*(1+161051*x)*(1-1771561*x)). - Vincenzo Librandi, Oct 30 2012

a(n) = (-1 +11^(6n-15) [phone]*11^(2n-9)*(1 -11^(2n-5)) +1330*11^(n-5)*(111 +111*11^(4n-10) -1637362*11^(2n-7))*(-1)^n) / 8011794142389510144000. - Bruno Berselli, Oct 30 2012